Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

Create An Account

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Equations

x + y = 10

Which is the greater quantity?

(a) 5y + 5x

(b) 50

Possible Answers:

It is impossible to tell from the information given

(a) and (b) are equal

(b) is greater

(a) is greater

Correct answer:

(a) and (b) are equal

Explanation:

x + y = 10

By the commutative property,

y + x = 10

By the multiplication property of equality,

$5 \left ( y + x \right )= 5\cdot 10$

By distribution,

5y + 5x = 5 0

Report an Error

Example Question #36 : How To Find The Solution To An Equation

is a positive number. Which is the greater quantity?

(a) $N ^{2}$

(b) $N ^{3} + N$

Possible Answers:

It is impossible to tell from the information given

(a) and (b) are equal

(b) is greater

(a) is greater

Correct answer:

(b) is greater

Explanation:

If N > 1 , then $N ^{3}+ N > N ^{3}= N ^{2} \cdot N > N ^{2} \cdot 1 = N ^{2}$

If N = 1 , then $N ^{3}+ N = 1 ^{3}+1 = 2 > 1 = 1^{2} = N ^{2}$

If 0 < N < 1 , then $N ^{3}+ N > N = N \cdot 1 > N \cdot N = N ^{2}$

Therefore, regardless of the value of , as long as is positive, $N ^{3} + N > N ^{2}$ , and (b) is greater.

Report an Error

Example Question #32 : Equations

$100 x + 100 y = \frac{1}{5}$

Which is the greater quantity?

(a) x + y

(b) 0.005

Possible Answers:

(b) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

(a) is greater.

Correct answer:

(b) is greater.

Explanation:

$100 x + 100 y = \frac{1}{5}$

From the multiplication property of equality,

$\frac{1}{100} \cdot \left ( 100 x + 100 y \right ) = \frac{1}{100} \cdot \frac{1}{5}$ .

By distribution,

$x + y = \frac{1}{500} = 0.002 < 0.005$ .

Report an Error

Example Question #33 : Equations

5t = 6u

Which is the greater quantity?

(a) | t |

(b) |u|

Possible Answers:

(a) is greater.

(b) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

Correct answer:

(a) is greater.

Explanation:

5t = 6u

$5t \div 5= 6u\div 5$

$t = \frac{6}{5} u$

Take the absolute value of both sides:

$\left |t \right|= \left | \frac{6}{5} u \right |$

$\left |t \right|= \frac{6}{5} \left | u \right | > \left | u \right |$

This makes (a) greater.

Report an Error

Example Question #39 : How To Find The Solution To An Equation

$4 A + 4 B = \frac{1}{25}$

10 C +10 D = 0.1

Which is the greater quantity?

(a) A + B

(b) C + D

Possible Answers:

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

(a) is greater.

Correct answer:

(a) and (b) are equal.

Explanation:

(a) $4 A + 4 B = \frac{1}{25}$

$\frac{1}{4} \cdot \left ( 4 A + 4 B \right ) = \frac{1}{4} \cdot \frac{1}{25}$

$A + B = \frac{1}{100 }$

(b) 10 C +10 D = 0.1

Rewrite as a fraction:

$10 C +10 D = \frac{1}{10 }$

$\frac{1}{10 } \cdot \left ( 10 C +10 D \right ) = \frac{1}{10 } \cdot \frac{1}{10 }$

$C + D= \frac{1}{100 }$

A + B = C + D

Report an Error

Example Question #40 : How To Find The Solution To An Equation

Define f(x) as follows:

$f(x) = \left\{\begin{matrix} x -3 \textrm{ if }x > 0 \\ x + 3 \textrm{ if }x \leq 0 \end{matrix}\right.$

Which is the greater quantity?

(a) f(5) + f(-5)

(b) f(0)

Possible Answers:

(b) is greater.

(a) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

Correct answer:

(b) is greater.

Explanation:

(a) f(5) can be evaluated by using the definition of for positive :

f (x) = x - 3

f (5) =5 - 3 = 2

f(-5) can be evaluated by using the definition of for nonpositive :

f (x) = x + 3

f (-5) =-5 + 3 = -2

Add: f(5) + f(-5) = 2 + (-2) = 0

(b) f(0) can be evaluated by using the definition of for nonpositive :

f (0) = 0 + 3 = 3

f (0) > f(5) + f(-5)

Report an Error

Example Question #41 : How To Find The Solution To An Equation

$\left \lfloor N \right \rfloor$ is defined as the greatest integer less than or equal to

$\left \lceil N \right \rceil$ is defined as the least integer greater than or equal to

N > 1 ; itself is not an integer.

Which is the greater quantity?

(a) $\left \lceil N \right \rceil \cdot \left \left \lfloor N+1 \right \rfloor$

(b) $\left \lceil N + 1 \right \rceil \cdot \left \left \lfloor N \right \rfloor$

Possible Answers:

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

(a) and (b) are equal.

Correct answer:

(a) is greater.

Explanation:

Let $x = \left \lfloor N \right \rfloor$ .

Then $\left \lfloor N + 1 \right \rfloor = x + 1$ .

Since is a noninteger, $\left \lceil N\right \rceil = x+ 1$ and $\left \lceil N + 1 \right \rceil = x+ 2$ .

(a) $\left \lceil N \right \rceil \cdot \left \left \lfloor N+1 \right \rfloor = \left ( x + 1 \right ) \left ( x + 1 \right ) = x^{2}+2x+1$

(b) $\left \lceil N + 1 \right \rceil \cdot \left \left \lfloor N \right \rfloor = (x+2) x = x ^{2}+ 2x$

(a) is greater than (b).

Report an Error

Example Question #711 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Define f (x) = 4 - 5x and g (x) = 5 - 4x .

can be any real number.

Which is the greater quantity?

(a) $(f \circ g) (x)$

(b) $(g \circ f) (x)$

Possible Answers:

It is impossible to tell from the information given.

(b) is greater.

(a) and (b) are equal.

(a) is greater.

Correct answer:

(b) is greater.

Explanation:

(a) $(f \circ g) (x) = (f ( g (x) ) = f (5-4x )$

Substitute 5-4x for :

f (x) = 4 - 5x

f (5-4x ) = 4 - 5 (5-4x )

$= 4 - 5 \cdot 5-\left ( -5 \right ) \cdot 4x$

= 4 -25+20x

= 20x-21

(b) $(g \circ f) (x) = g(f(x)) = g (4-5x)$

Substitute 4-5x for :

g (x) = 5 - 4x

g (x) = 5 - 4(4-5x)

$= 5 - 4 \cdot 4- \left ( - 4 \right ) \cdot 5x$

= 5 - 16 +20x

= 20x - 11

-11 > -21 , so regardless of the value of , 20x - 11 > 20x - 21 , and (b) is greater.

Report an Error

Example Question #42 : How To Find The Solution To An Equation

Veronica and Stephanie bought sweaters of the same type, but at different stores. Veronica bought hers for $\$60.00$ at Markham's; Stephanie bought hers for $\$75.00$ at Schuster's. Veronica got a better discount rate than Stephanie, and she has been bragging about it.

Which is the greater quantity?

(a) The price of the sweater at Markham's before discount

(b) The price of the sweater at Schuster's before discount

Possible Answers:

(a) and (b) are equal.

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

Correct answer:

It is impossible to tell from the information given.

Explanation:

We show that the question cannot be answered with certainty by taking two sample cases.

Case 1: The sweaters cost $\$100.00$ at both stores.

Veronica saved $\$100.00 - 60.00 = \$40.00$ and got a $40\%$ discount rate. Stephanie saved $\$100.00 - 75.00 = \$25.00$ and got a $25\%$ discount rate.

Case 2: The sweater cost $\$100.00$ at Markham's and $\$90.00$ at Schuster's.

In this case Veronica saved $\$100.00 - 60.00 = \$40.00$ and got a $40\%$ discount rate. Stephanie saved $\$90.00 - 75.00 = \$15.00$ and got a discount rate of $\frac{15}{90} \times 100 = 16 \frac{2}{3} \%$ .

Report an Error

Example Question #43 : How To Find The Solution To An Equation

Define $g (x) = x^{4} + 2x^{2} - 1$ .

Which is the greater quantity?

(a) g(5)

(b) g(-5)

Possible Answers:

(a) is greater.

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

Correct answer:

(a) and (b) are equal.

Explanation:

(a) $g (x) = x^{4} + 2x^{2} - 1$

$g (5) = 5^{4} + 2 \cdot 5^{2} - 1$

$= 625 + 2 \cdot 25 - 1$

= 625 + 50 - 1

= 674

(b) $g (x) = x^{4} + 2x^{2} - 1$

$g (-5) = (-5)^{4} + 2 \cdot (-5)^{2} - 1$

$= 625 + 2 \cdot 25 - 1$

= 674

g (5) = g (-5)

Report an Error

View Tutors

Pushpendra
Certified Tutor

university of allahabad, Bachelor of Science, Mathematics.

View Tutors

Robert
Certified Tutor

University of North Carolina at Chapel Hill, Bachelor in Arts, English. North Carolina Central University, Master of Arts, En...

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Phoenix, MCAT Tutors in Los Angeles, Reading Tutors in Phoenix, Biology Tutors in Denver, Math Tutors in Dallas Fort Worth, MCAT Tutors in Atlanta, Physics Tutors in Houston, ACT Tutors in Boston, Reading Tutors in Houston, Computer Science Tutors in Los Angeles

Popular Courses & Classes

ISEE Courses & Classes in Washington DC, MCAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Boston, GRE Courses & Classes in Phoenix, LSAT Courses & Classes in Washington DC, GRE Courses & Classes in San Diego, Spanish Courses & Classes in New York City, MCAT Courses & Classes in San Diego, ACT Courses & Classes in Philadelphia, SSAT Courses & Classes in Boston

Popular Test Prep

LSAT Test Prep in Washington DC, ISEE Test Prep in Phoenix, ISEE Test Prep in Denver, ISEE Test Prep in Philadelphia, GMAT Test Prep in San Diego, GRE Test Prep in New York City, LSAT Test Prep in Miami, MCAT Test Prep in Los Angeles, MCAT Test Prep in Denver, LSAT Test Prep in Chicago

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #31 : Equations

Example Question #36 : How To Find The Solution To An Equation

Example Question #32 : Equations

Example Question #33 : Equations

Example Question #39 : How To Find The Solution To An Equation

Example Question #40 : How To Find The Solution To An Equation

Example Question #41 : How To Find The Solution To An Equation

Example Question #711 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #42 : How To Find The Solution To An Equation

Example Question #43 : How To Find The Solution To An Equation

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: